Introduction to radians | Unit circle definition of trig functions | Trigonometry | Khan Academy

[@stevedl3150]

I think radians should be taught from Primary School, rather than degrees. Radians are obviously intrinsic to the circle, whereas degrees are not. Alas, I still find it difficult to think in terms of radians.

[@lakshmipraba220]

Same!

[@kalaiselvanrajasekaran8352]

The concept is so easy yet it is still being a great task to understand the radians.

[@PenandPaperScience]

This is the core argument I make in my video covering Radians! It's a measure that incorporates only intrinsic properties of the circle!

[@isavenewspapers8890]

Have you heard of the number tau? It's represented with the Greek letter tau, which looks like this: τ τ is the ratio of a circle's circumference to its radius. This makes it 2 times π, or about 6.28. Using τ, one full rotation is τ radians. One-half of a full rotation is τ/2 radians. One-third of a full rotation is τ/3 radians. Whatever fraction of a full rotation you do, its measurement in radians is that same fraction of τ. If it helps, you can think of radians in terms of τ.

[@vsatrawada]

⁠

[@pboytrif1]

2:46 The moment I decided I liked the video... "I'm gonna attempt to draw a circle here....... *wobbly circle*...... not baaaaaad"

[@raithigovender195]

aw. I was so excited to comment RAAAADIUSSSES then I saw the comments section and was like...yeah nvm

[@slowloris2996]

I’m in the exact same situation.

[@lcveiris]

Ikr😂

[@ruguoserliegise2716]

same

[@arjunsogarwal6099]

RAIDUSESESESESESESESESESESES, wow what a word

[@The_Pariah]

That was a very good way of explaining this. I've been out of high school long enough to have forgotten a lot of trig. Now that I'm doing programming, this stuff is needed and these refresher videos really help (especially when they're well done like this one).

[@Jam-nh5wb]

U saying radiuseseseseseseseses drove me insane, I literally couldn’t pay attention to the video 😂

[@Faith._.M]

I was abt to say that

[@sarahkenza3883]

he literally wrote down the plural, it radians... IT'S RADIANS

[@Ferdinaand]

same and i was playing at 1.25 so it made it worse

[@BobBob-uv9fq]

Lol you’re correct ,but he’s explaining it well

[@furqaanilahi8078]

@@sarahkenza3883 radii?

[@saifullahrahman]

98% comments = radiuseseseses

[@olivermiller8943]

More like 60

[@sirwaffle4006]

i never appreciate your circle drawing skills until i have to draw a circle myself

[@Cesariono]

The definition of the radian suddenly makes so much sense. I used radians in my calculations but I never really understood why they even bothered. Now my mind has been blown.

[@sunnylefabulous6736]

i knew from the moment our teacher started explaining this in class there'd be our lord and saviour, Sal Khan, who would explain this much, much better

[@timothycarney2951]

Radiuseseses?!? Radii! Radii! Radieye! RADI👁!

[@KaushalKumar-vq8kb]

Absolutely!

[@CreationTribe]

Yup - which is weird since I've heard him say "radii" multiple times in other videos. Is he just being funny? I don't get it.

[@alimuhammed9173]

RADIUESESESESE

[@feelgood_cinematic1919]

i thought i was the only one!!! lol

[@user-rf4vc7mt4d]

micheal jordan It's been a week, but... You don't have to watch it to understand, but it would definitely help

[@Neel-ff4mn]

2:23 To sum DEGREE! Lol!

[@ultrainstinctx6135]

Ali Muhammed I

[@roblox_pandagameryt8612]

Sub to me and i sub to u~

[@tejasbinu5025]

What are RADIUESESESESE?

[@fantasaicproductions7612]

listen to that part at video speed x2 and you'll find out what it means... its means hes part snake or should i say slytherin....

[@LittleWhole]

Radii

[@muninnhugin]

very helpful! cracked me up every time he said radiuseseseses =)

[@amrsaleh1342]

"just to show u this isn't voodo" 😂😂😂😂

[@ruguoserliegise2716]

Had me rolling

[@mischief9499]

hahahah

[@poochihuku3701]

The kinds of things that make me a stickler to learn from these videos

[@namraaah271]

if u still don't get it don't worry just read the textbook or whatever and keep trying to understand and then watch the video...i swear you'll get it.I have been spending the whole day trying to understand this and now i finally get it.time taken-approx 6 hours.dude...

[@jar0bi]

I'm taking a trigonometry class right now and this explains so much thank you

[@saflanix]

My teacher recorded a few videos during quarantine and I never watched them cuz these are so much better☺️

[@DopeBoysClan]

I just had a "I UNDERSTAND" moment. I would have not resorted to these videos, along with the rest of the people here had teachers derived the meaning to mathematical concepts, instead of saying "here it is, use it". The amount of stupidity evident in today's education is absolutely mind-blowing, unfathomable. I can only but barley understand the teachers motives for not deriving and explaining where particular principles come from, that of which is they don't care, they want the paychecks and to go home. Fuck society man.

[@namraaah271]

where u from?how u doin now

[@valejandro1771]

@@namraaah271 HOPE he's ok. It's been a lot of time :0

[@yeo1913]

You haven't lost yet and you have more to achieve

[@ellipszia]

radiuseseseseseseseseses

[@sourabhuwusingh]

A great explanation! Khan Academy is a great place to learn.

[@AndewMole]

On average he said "ses" 3.333 times. 4:32, 5:09, 5:50, 6:22, 6:44, 6:46, 7:07, 7:13, 8:36 4, 1, 5, 4, 3, 3, 5, 2, 3

[@callumsimpson1278]

What program do they use for the drawing?

[@meightyalliu5408]

this video is clear! save my life from digging into textbook:P

[@primaryaccount1410]

7:34 degrees-es-es

[@benzonex]

radiuseseses...

[@tracker1312]

This was explained amazingly well. I don't think any of my teachers ever explained this, neither in grade school or college.

[@PenandPaperScience]

I wanted to plug my own video attempt where I explain this concept, but I have nothing to add. Great video! :D

[@bluewolf8085]

I learned alot today, Radiuseseseses are very important...😂😂😂😂

[@johnydove4402]

this is great GOD BLESS

[@EmpowerQuest1]

❤I know, the video was uploaded ten years ago but it had something that made me keep watching it till the end. ❤

[@ThomasGardner12321]

Thanks this is going to help me with my Core 2 A-level exams alot! :)

[@XtremeKillah101]

radiuseseseseseses

[@rishab5501]

Nobody: Sal: I think it's intuitive, cause in an intuitive response I'll intuitively intuitive. Me: A video on what intuitive means?

[@TechnicalGarg]

That was really nice. Many teachers just tell to remember this without informing about proper concept. But u r gr8.. Thank you a lot❤

[@svengunther7653]

Clear, easy, with background. Thanks :)

[@vsatrawada]

I was so focused in much in math that I forgot you teach like everything in the world.

[@chithienle9790]

your lectures are very easy to understan

[@Medi-Nor]

This video very helpful. 👍🏻

[@minameehan617]

Thank you so much your video made so much more sense than my teacher 🙏

[@jcutey]

Fantastic explanation. I study as well as teach physics. I couldn't have done it better myself. Congratulations.

[@angmori172]

Awesome, thanks! Finally got radians!

[@herwin4946]

Thank you! I was so confused with the radian, but now I understand much more now.

[@HuckleberryHim]

I got ~57.2957795131 degrees per radian using a calculator and pi as far as it would go (3.141592653589793).

[@drtoro]

how successfull are you to make things easier to understand..

[@theflash9735]

THIS IS SOOOOO GOOD !.... AND IT'S 7 YEARS AGO !!!!

[@271skippy]

I swear, I could never have gotten anywhere in math were it not for Khan Academy and Teaching Textbooks

[@charlieromeo7663]

Thanks for the explanation.

[@Achw3l]

Very well explained!! Logical and easy to follow :)

[@noobtrader454]

how neatly u write on this is mind blown

[@MerlinZuni]

Thanks for this explanation. I'm taking a coding class and this was very helpful.

[@laxmandesai573]

I love the way u teach!! wish all the teachers were just like u

[@nitinchawla8854]

You made a good video...👍 Made me understand the radian concept.

[@TheAmazingFocus]

He already did a video on Tau versus Pi. He probably doesn't want to introduce too much at once when introducing the concept of radians. Though an aside about it in a future angular measure would be nice!

[@Ash-ec4ip]

I respect u a lot.... Thank u❤️

[@teenatkhan1695]

Thank Gosh this exists

[@frannylissetrodriguez4066]

Thank you so MUCH !

[@yplayergames7934]

Even though it's a 11 years vídeo, this explained radians very well that I understand very clearly

[@MrWarmWeather]

great video. best I've seen on the subject so far. thanks!

[@samcaddy8544]

Explained brilliantly

[@GuruprakashAcademy]

hey sal what microphone u are using. I am also making videos. Please let me know. Thans in advance

[@poweruser64]

thanks for all the -radiuseses- radii

[@krishshah3974]

Having motivation behind ideas (rather than just memorizing them) makes Khan Academy amazing!

[@Propapanda0213]

Nice video! Straightforward and easy to understand

[@vihaansinghhh3034]

6:23 RADIUSESESESESESESESESESESESESESEES..".... till 1 min 😂😂😂🤣

[@lucy2459]

thank you so much for making this so clear and being so friendly :) this really helped me. my maths teacher just gets angry when i don't understand things so stuff like this is a godsend :D

[@lemonrev]

radians something i dont think everyone is associated with the term and i like it how your thinking out side the box with the alien thing, with looking at circles, Do you think this actually should be the model for looking at degreese in general in stead of useing our term the degreese of ?

[@exceptionalchris]

"This isnt some voodoo" classic.

[@teenatkhan1695]

Chris Btw what is it😂

[@EmmyKhan]

"let's cut to the chase: 2:43"

[@VictorAndScience]

Whenever he said sixty symbols I couldn't stop thinking about Brady's Channel.

[@chissstardestroyer]

On the topic of using Pi in division; that in and of itself is usually why people round it to 3.14, to the hundredths place, otherwise it takes literally forever, or almost, to reach the termination point/end point, of the formula. As you pointed out, Mr. Khan, a very interesting way to convert them; actually you have a better time dividing by zero than dividing by pi to the final digit.

[@areeb9781]

amazingly explained. just wondering what radian is ? read some books but didn't get the satisfied answer and you really solved my problem. thanks for sharing :)

[@abdosalah4337]

So what is radian cuz i dont understand

[@pranjalpandey7020]

Great video really informative.Great Easter egg

[@Sadin15]

It is more commonly known as Arc Length. It is represented with an S and can be found using S = theta * radius

[@yaronzaret9549]

Great video Sal, keep them coming!

[@gottfriedwiggles3230]

Very nice explanation! Thank you

[@SoundPeaks]

thanks, what tools allows you to make video like that? How do you draw and move mouse so precisely?

[@mmohan692]

Wow nice video keep it up .

[@Theiftanlazx]

yay i understand it much better

[@RaharijaoDavid]

Just wanted to ask , why did you remove the r from "2(pie)×r"? , if you could or anybody could answer me , I'd be grateful

[@atanaspetkov9298]

because r=1 and 2(pi)x1=2(pi)

[@RaharijaoDavid]

ok thx

[@HeyKevinYT]

2:40 start here

[@calcul8er205]

Radii!!

[@nikhilparaggarapinhilik4733]

He is good in explaining really Much better than me😫😂

[@oujui]

If a right degree angle was actually measured as 100 degrees, our life would be so much easier

[@MAYONNAISEMOOSE]

How?? I think itll be chaotic. Yes ik, 5 years ago.

[@chissstardestroyer]

If you divide by pi you'll be dividing forever, unless you abrieviate pi at some point, because pi is a non-terminating, non-repeating decimal, so it goes on and on forever. In fact, for many decades they've had computers just trying to calculate the termination of pi.

[@richabose6844]

this guy really has some sense of humour 😀😀

[@fromexoplanet21]

Amazing👏👌

[@EmmaRunningWeb]

Thank you!

[@DHARMIK_M]

What Slate do you use

[@rashedalam3450]

That's a better circle than i've ever drawn

[@Kenneth_H_Olsen]

yeah. the interesting thing is that the formula for radians is 2* pi * r. Making it seem that one needs 2 pi then multiply with the radius. but actually it is not 2 of Pi, but 2 radiuses that make one diameter. Diameter * pi = 360 degrees. and r * pi = 180 degrees . the formula should be 2r* pi. If the radius is 0.5 units then one can wrap 6.28 radiuses around the circumference (or 2Pi), but 3.14 diameters around the circumference (or Pi, diameter being 2r or 2*0.5 = 1) . Just being picky but I think it is important . why would one need 2 rotations of pi, and a radius, when it is the double radius or diameter that is defining the circumference with pi ? would it be correct to say this : 1. Radius is the number of times a radius is wrapped around the circumference . 2. find the radian of 3 degrees. 180 / 3 = 60 Pi radian = 180 Pi radian / 60 = 180 / 60 0.05 rad = 3 degrees .

[@tfalaschini]

The order of the factors doesn't affect the product ;)

[@tfalaschini]

The order of the factors doesn't affect the product. ;)

[@mmohan692]

We want more videos like tz

[@ramillax5478]

THANKS

[@CaptTerrific]

While that would be very nice, it is an unfortunately reality that Kahn's lessons should help students out in the real world... and since the rest of the world is stuck on the idea of using Pi and only Pi, it would probably be a disservice to students to teach them the Tau method (i know it is very simple to translate from one to the other, but not for those who have never been exposed to radians/trig before)

[@Cryztaliser]

excellent video

[@6xsnspsychotik963]

god bless you guys

[@lemon23]

7:34 degreeeseseses... man's got crazy xd

[@abdosalah4337]

Hey dude can u just tell me what is the meaning of radians cuz i dont rly understand

[@hazleenazlee506]

Thanks

[@f4nte]

Nice.